Natural movement to polygon Hair
There is something wrong with how you weight painted the mesh. If I remember correctly, if you weight painted it at "the roots", the part of the mesh that is not weight painted should move. Or it could be the other way around. So just to be sure, here are some videos to help you out on the softbodies issue.

https://www.youtube.com/watch?v=j2tM_LS8jIA

https://www.youtube.com/watch?v=e1lHca7I3So

Hopefully, these videos can lead you into the right direction.